Thin and Thick Cylinders
Exam Duration: 45 Mins Total Questions : 20
Longitudinal stresses act - to the longitudinal axis of the shell
- (a)
perpendicular
- (b)
parallel
- (c)
either of the above
- (d)
None of these
In case of seamless shell, the change in volume (dv) is given by
- (a)
\(\delta V=\frac { pdV }{ 2tE } \left( \frac { 5 }{ 2 } -\frac { 2 }{ m } \right) \)
- (b)
\(\delta V=\frac { pdV }{ 4tE } \left( \frac { 5 }{ 2 } -\frac { 2 }{ m } \right) \)
- (c)
\(\delta V=\frac { p{ d }^{ 2 }V }{ 2tE } \left( \frac { 7 }{ 2 } -2\mu \right) \)
- (d)
\(\delta V=\frac { p{ d }^{ 2 }V }{ 2tE } \left( \frac { 5 }{ 2 } -2\mu \right) \)
In a thin shell, circumferential stress (\({ \sigma }_{ c }\))is given by
- (a)
\({ \sigma }_{ c }=\frac { pd }{ 2t{ \eta }_{ l } } \)
- (b)
\({ \sigma }_{ c }=\frac { pd }{ 2t{ \eta }_{ c } } \)
- (c)
\({ \sigma }_{ c }=\frac { pd^2 }{ 2t{ \eta }_{ c } } \)
- (d)
\({ \sigma }_{ c }=\frac { pd }{ t{ \eta }_{ l } } \)
In thin cylinders, the radial stress in the wall thickness is
- (a)
zero
- (b)
negligibly small
- (c)
not negligible
- (d)
Any of these
In thick cylinders, the radial stress in the wall thickness
- (a)
is zero
- (b)
negligibly small
- (c)
not negligible and varies from the inner surface to the outer surface
- (d)
None of the above
Which of the following assumptions are made while solving problems on thick cylinders using Lame's theory?
- (a)
The material is homogeneous and isotropic
- (b)
Plane sections perpendicular to the longitudinal axis of the cylinder remains plane after the application of internal pressure
- (c)
Both (a) and (b)
- (d)
None of the above
Consider the following statements:
In a thick walled cylindrical pressure vessel subjected to internal pressure, the tangential and radial stresses are
1. minimum at outer side.
2. minimum at inner side.
3. maximum at inner side and both reduce to zero at outer wall.
4. maximum at inner wall but the radial stress reduces to zero at outer wall.
Which of the statements given above is/are correct?
- (a)
1 and 2
- (b)
1 and 3
- (c)
1 and 4
- (d)
Only 4
In case of a column
- (a)
one end is hinged and other end fixed
- (b)
one end is fixed and other end free
- (c)
both ends are fixed rigid1y
- (d)
both ends are hinged
Match List I with List II and select the correct answer using the code given below the lists.
List I (Long column) |
List II (Critical load) |
P. Both ends hinged. Q. One end fixed and other end free. R. Both ends fixed. S. One end fixed and othe rend hinged. |
\(1.\quad { \pi }^{ 2 }\frac { El }{ { 4l }^{ 2 } } \) \(2.\quad { 4\pi }^{ 2 }\frac { El }{ { l }^{ 2 } } \) \(3.\quad { 2\pi }^{ 2 }\frac { El }{ { l }^{ 2 } } \) \(4.\quad { \pi }^{ 2 }\frac { El }{ { l }^{ 2 } } \) |
Codes
- (a)
P Q R S 1 2 3 4 - (b)
P Q R S 3 2 1 4 - (c)
P Q R S 2 4 1 3 - (d)
P Q R S 4 1 2 3
The radius of gyration of a circular column of diameter d is
- (a)
\(\frac{d}{4}\)
- (b)
\(\frac{d}{2}\)
- (c)
\(\frac{d^2}{16}\)
- (d)
\(\frac{d^2}{4}\)
Two springs of stiffness k1 and k2 respectively are connected in series, the stiffness of composite spring is
- (a)
k= k1 x k2
- (b)
k= k1 + k2
- (c)
\(K=\frac { { K }_{ 1 }{ K }_{ 2 } }{ { K }_{ 1 }{ +K }_{ 2 } } \)
- (d)
\(K=\frac { { K }_{ 1 }{ +K }_{ 2 } }{ { K }_{ 1 }{ K }_{ 2 } } \)
A thick cylinder of 150 mm outside and 100 mm inside radius is subjected to an external pressure of 30 MN/m2.
(I) Constant of Lame's equation are
- (a)
b = -540000, a = -54
- (b)
b = -54, a = -540000
- (c)
b = -54, a = 0
- (d)
b = 0, a = 54
A thick cylinder of 150 mm outside and 100 mm inside radius is subjected to an external pressure of 30 MN/m2.
Hoop stress at inner surface is
- (a)
108 N/mm2
- (b)
100 N/mm2
- (c)
91 N/mm2
- (d)
121 N/mm2
A seamless spherical shell is of 8 m internal diameter and 4 mm thickness. It is filled with fluid under pressure until its volume increases by 50 cc. If E = 2 x 105 N/mm2, \(\mu\) = 0.3, then determine
(I) Volumetric strain is
- (a)
186.5 x 10-9
- (b)
190 x 10-9
- (c)
170 x 10-9
- (d)
None of these
A seamless spherical shell is of 8 m internal diameter and 4 mm thickness. It is filled with fluid under pressure until its volume increases by 50 cc. If E = 2 x 105 N/mm2, \(\mu\) = 0.3, then determine
Internal fluid pressure is (N / mm-2)
- (a)
40 x 10-6
- (b)
30 x 10-6
- (c)
35 x 10-6
- (d)
28 x 10-6
A spherical vessel of steel (di = 600 mm, t = 10 mm) is fill with water under pressure of 6 MPa. 446 x 103 mm3 volume of water is let out to reduce the pressure. If k = 2 GPa for water, ESteel = 200 GPa, then Poisson's ratio is
- (a)
0.7
- (b)
0.8
- (c)
0.25
- (d)
0.30
A mild steel strut is of single angle section 100 mm x 75 mm x 8 mm. Its length is 3 m with both ends fixed.
The section has 1.336 m2 as area of cross-section. Its radius of gyration about XX, YY, UU and VV axes are 31.4 mm, 21.8 mm, 34.8 mm and 15.9 mm respectively. Constants in formula may be taken as a=\(\frac{1}{7500}\)and fc = 330 N/mm2. Take FOS = 3 and by Rankine formula the maximum safe load for column is
- (a)
70 kN
- (b)
67 kN
- (c)
80 kN
- (d)
None of these
column 2.5 m long is pin-connected at both ends. It has 50 mm x 100 mm rectangular cross-section. Young's modulus of material is 2.0 x 105 MPa. Determine
The slenderness ratio
- (a)
80
- (b)
87
- (c)
89
- (d)
98
column 2.5 m long is pin-connected at both ends. It has 50 mm x 100 mm rectangular cross-section. Young's modulus of material is 2.0 x 105 MPa. Determine
Axial stress
- (a)
300 MN/m2
- (b)
263.2 MN/m2
- (c)
100 MN/m2
- (d)
137.5 MN/m2
column 2.5 m long is pin-connected at both ends. It has 50 mm x 100 mm rectangular cross-section. Young's modulus of material is 2.0 x 105 MPa. Determine
If FOS = 2.5, then safe load is (MN)
- (a)
1.21
- (b)
2.13
- (c)
0.52
- (d)
0.72